Anti-war activist Medea Benjamin is led away after heckling Barack Obama during his counter-terrorism speech at the National Defense University in Washington. Photograph: Win Mcnamee/Getty Images

In the past week, both President Barack Obama and First Lady Michelle Obama have been interrupted by what some call hecklers, but I prefer to call protesters. I was the one who interrupted President Obama's speech at the National Defense University with my impassioned questions about drone strikes and Guantánamo.

After my interventions, the president graciously replied, "That woman's voice is worth listening to." But when the First Lady was confronted by a lesbian woman speaking up about President Obama's failure to protect gay people in the workplace, as he had promised, she reacted angrily.

As someone who has witnessed (and participated in) many interruptions, here are some examples of what I consider good responses.

Several years ago, I was once at a large conference when Los Angeles Mayor Antonio Villaraigosa was speaking. Suddenly, a group of black and Latina women interrupted him, shouting out about the need for more buses in their communities, instead of the city plan to spend many millions expanding the metro. The mayor first tried to talk over them, then the audience tried to drown them out, but the women kept shouting. Villaraigosa quieted the audience and then said:

"Look, it takes a lot of courage for these people to get up in a big audience and promote a cause they believe in. Let's give them a round of applause."

It was a brilliant way to recognize the passion of the protesters, but turn around the dynamic so he could continue his talk.

At an event in 2007, French Foreign Minister Bernard Kouchner gave a speech in Washington, DC on the heels of remarks that the US and France should prepare for a possible war with Iran. US peace activists, who had been trying hard to prevent war, were appalled. A group of us spoke out at the event and unfurled a banner in French reading: "Va-t-en-guerre san frontieres" (warmonger without borders) – playing off the fact that Kouchner was one of the founders of Doctors Without Borders. Security guards pulled us out of room, but Kouchner asked them to let us back in so he could address our concerns directly, which he did.

When the talk was over, he came over to shake our hands, and even asked if he could have the banner as a souvenir, since he thought it was very clever. "We are used to rowdy audiences in France," he laughed, "so you made me feel right at home."

Most protests are coming from frustrated citizens confronting the powerful and are part of a much larger strategy for change. In 1964, civil rights activists, including Bayard Rustin and James Farmer, shouted down President Lyndon Johnson during his speech at the World's Fair, calling for passage of the Civil Rights Act. They were arrested, but their intervention was celebrated as part of a much larger nonviolent strategy of the civil rights movement.

Sometimes, it's not the powerful who are interrupted, but simply someone with a different viewpoint. Speaking at a university, I was once interrupted by a group of students who disagreed with my views on Israel/Palestine. My response was to invite them on stage to use the mic so they could be heard by all. They did, and when they were finished, I thanked them, addressed their issues according to my – very different – perspective; I said I hoped they'd stick around for the Q&A, so we could keep the conversation going.

Speaking out to express our political beliefs or show disapproval of those in power is part of the venerable practice of nonviolent civil disobedience. The tactic might be considered impolite and it disrupts business as usual, but hopefully, it helps push forward a larger debate on issues of great importance to society.

At a campaign event when Obama was first running for president, someone asked him what he would do about the Middle East. Obama repeated the legendary story about President Franklin Delano Roosevelt meeting with labor leader A Philip Randolph about workers' rights. Reportedly, FDR listened intently, then replied:

I agree with everything you have said. Now, make me do it.

Speaking out on the rare occasions we have to interact with the powerful is just that: pushing those in power to do the right thing.